Adaptive-Multilevel BDDC and its parallel implementation

We combine the adaptive and multilevel approaches to the BDDC and formulate a method which allows an adaptive selection of constraints on each decomposition level. We also present a strategy for the solution of local eigenvalue problems in the adaptive algorithm using the LOBPCG method with a precon...

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Bibliographic Details
Published in:Computing 2013-12, Vol.95 (12), p.1087-1119
Main Authors: Sousedík, Bedřich, Šístek, Jakub, Mandel, Jan
Format: Article
Language:English
Subjects:
Algorithms
Artificial Intelligence
Computer Appl. in Administrative Data Processing
Computer Communication Networks
Computer Science
Decomposition
Eigenvalues
Information Systems Applications (incl.Internet)
Interfaces
Iterative methods
Methods
Parallel processing
Software Engineering
Studies
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Summary:We combine the adaptive and multilevel approaches to the BDDC and formulate a method which allows an adaptive selection of constraints on each decomposition level. We also present a strategy for the solution of local eigenvalue problems in the adaptive algorithm using the LOBPCG method with a preconditioner based on standard components of the BDDC. The effectiveness of the method is illustrated on several engineering problems. It appears that the Adaptive-Multilevel BDDC algorithm is able to effectively detect troublesome parts on each decomposition level and improve convergence of the method. The developed open-source parallel implementation shows a good scalability as well as applicability to very large problems and core counts.
ISSN:0010-485X
1436-5057
DOI:10.1007/s00607-013-0293-5